Lys Mousset's first-half goal punished Nicolas Pepe's earlier close-range miss and condemned the Gunners to a second defeat in nine Premier League games.
Unai Emery claimed his side did not deserve to lose but former Manchester United defender Evra disagreed and attacked the team's character.
In an appearance on Sky Sports, the retired left-back claimed the club's shortcomings were ingrained and became clear to Robin van Persie following his move from Arsenal to Old Trafford in 2012.
"I used to call them 'my babies' 10 years ago and they are still, when I look at them, my babies. That's the truth," Evra said.
"I'm not being disrespectful when I say that. It's just the feeling I get from this team. They look pretty, they look good, but they don't look like a winning team. They just play good football.
"I was so happy to play against Arsenal because I knew I was going to win.
"Even when Robin van Persie came, the first day I shook his hand and said 'welcome to a man's club'.
"At the beginning he was upset but after one month he said 'you're completely right, Patrice'. That's my feeling. [Matteo] Guendouzi is a player who was playing in the French second league - and he was even not playing regularly - and he's the best player in this team.
"I know some legends are fuming when they see [Granit] Xhaka is captain of Arsenal.
"I respect [Pierre-Emerick] Aubameyang, [Alexandre] Lacazette, but you see if those guys don't score, they're in trouble. Nothing has changed."
Arsenal lies fifth in the Premier League, two points adrift of the Champions League places.